Enter your search terms Submit search form
	Web pdp-10.trailing-edge.com

SUBROUTINE DRTMI

PURPOSE
   TO SOLVE GENERAL NONLINEAR EQUATIONS OF THE FORM FCT(X)=0
   BY MEANS OF MUELLER-S ITERATION METHOD.

USAGE
   CALL DRTMI (X,F,FCT,XLI,XRI,EPS,IEND,IER)
   PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT.

DESCRIPTION OF PARAMETERS
   X	  - DOUBLE PRECISION RESULTANT ROOT OF EQUATION
	    FCT(X)=0.
   F	  - DOUBLE PRECISION RESULTANT FUNCTION VALUE
	    AT ROOT X.
   FCT	  - NAME OF THE EXTERNAL DOUBLE PRECISION FUNCTION
	    SUBPROGRAM USED.
   XLI	  - DOUBLE PRECISION INPUT VALUE WHICH SPECIFIES THE
	    INITIAL LEFT BOUND OF THE ROOT X.
   XRI	  - DOUBLE PRECISION INPUT VALUE WHICH SPECIFIES THE
	    INITIAL RIGHT BOUND OF THE ROOT X.
   EPS	  - SINGLE PRECISION INPUT VALUE WHICH SPECIFIES THE
	    UPPER BOUND OF THE ERROR OF RESULT X.
   IEND   - MAXIMUM NUMBER OF ITERATION STEPS SPECIFIED.
   IER	  - RESULTANT ERROR PARAMETER CODED AS FOLLOWS
	     IER=0 - NO ERROR,
	     IER=1 - NO CONVERGENCE AFTER IEND ITERATION STEPS
		     FOLLOWED BY IEND SUCCESSIVE STEPS OF
		     BISECTION,
	     IER=2 - BASIC ASSUMPTION FCT(XLI)*FCT(XRI) LESS
		     THAN OR EQUAL TO ZERO IS NOT SATISFIED.

REMARKS
   THE PROCEDURE ASSUMES THAT FUNCTION VALUES AT INITIAL
   BOUNDS XLI AND XRI HAVE NOT THE SAME SIGN. IF THIS BASIC
   ASSUMPTION IS NOT SATISFIED BY INPUT VALUES XLI AND XRI, THE
   PROCEDURE IS BYPASSED AND GIVES THE ERROR MESSAGE IER=2.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   THE EXTERNAL DOUBLE PRECISION FUNCTION SUBPROGRAM FCT(X)
   MUST BE FURNISHED BY THE USER.

METHOD
   SOLUTION OF EQUATION FCT(X)=0 IS DONE BY MEANS OF MUELLER-S
   ITERATION METHOD OF SUCCESSIVE BISECTIONS AND INVERSE
   PARABOLIC INTERPOLATION, WHICH STARTS AT THE INITIAL BOUNDS
   XLI AND XRI. CONVERGENCE IS QUADRATIC IF THE DERIVATIVE OF
   FCT(X) AT ROOT X IS NOT EQUAL TO ZERO. ONE ITERATION STEP
   REQUIRES TWO EVALUATIONS OF FCT(X). FOR TEST ON SATISFACTORY
   ACCURACY SEE FORMULAE (3,4) OF MATHEMATICAL DESCRIPTION.
   FOR REFERENCE, SEE G. K. KRISTIANSEN, ZERO OF ARBITRARY
   FUNCTION, BIT, VOL. 3 (1963), PP.205-206.